Various phenomena are represented as binary decisions in which one of two decision symbols (such as yes and no) is characterized by one probability (Pr) and the other symbol is charaterized by a probability (1-Pr). The less likely symbol is typically referred to as the less (or least) probable symbol LPS whereas the other symbol is referred to as the more (or most) probable symbol MPS.
Generally, the probability Pr is initially determined as an estimate from previous data or an initial estimate based on intuition, mathematics, assumptions, statistics collection, or the like. This estimate may be correct at some times or under some conditions but may not reflect the true probabilities at other times or under other conditions.
In some prior technology, the probabilities are determined before data processing--such as data encoding--and remain fixed. In such prior art, results obtained may be inaccurate because they are not based on current actual data.
In other prior technology, probabilities are evaluated which are intended to reflect data history. One article which discusses such prior art is included in the IBM Technical Disclosure Bulletin in volume 22, No. 7, December 1979, pps. 2880-2882, and is entitled "Method for Coding Counts to Coding Parameters" (by G. G. Langdon, Jr. and J. J. Rissanen). The article states that it is desired to detect changes in the symbol probabilities from observed symbol occurrences, and modify the LPS probability q accordingly. One approach suggested by the article is to change q to reflect the number of counts of one symbol divided by the total number of symbols counted during a symbol string. That is, if k is the counts for one symbol and n is the number of counts for both symbols, symbol probability is changed based on k/n.
Another article by Langdon and Rissanen, "Compression of Black/White Images with Arithmetic Coding", IEEE Transactions on Communications, volume COM-29, No. 6, June 1981, discusses adapting probabilities in an arithmetic coding environment. In discussing adaptation to nonstationary statistics, the IEEE article proceeds on page 865 as follows: "Suppose that we have received r (consecutive) 0's at a state z and our current estimate of the probability of symbol s(i) being 0 is p=c0/c . . . where c0 is a count defined as c(0.vertline.z,s(0), . . . , s(t)) and c is a count defined as c(z,s(0), . . . , s(t)). We receive symbol s(i). If s(i) is 0, we test: p'(r+1).gtoreq.0.2? If yes, we regard the observation as being consistent with our estimate of p, and we update c0 and c to form a new estimate . . . If, however, p'(r+1)&lt;0.2, the observation is likely an indication of changed statistics and we ought to be prepared to change our estimates to a larger value of p. We do this by halving the counts c0 and c before updating them by 1. We do the same confidence test if s(i) if 1 using the probability p(r) . . . In reality, for the sake of easier implementation, we put suitable upper and lower bounds on the count for the less probable symbol for each skew value Q(s) to indicate when to halve or not the counts. " In describing the Q(s) value, it is noted that the IEEE article discusses the approximating of the less probable symbol probability to the nearest value of 2.sup.-Q(s) where Q(s) is an integer referred to as the "skew number."
Other prior technology includes U.S. Pat. Nos. 4,467,317, 4,286,256, and 4,325,085 and an IBM Technical Disclosure Bulletin article in volume 23, No. 11, April 1981, pps 5112-5114, entitled "Arithmetic Compression Code Control Parameters Approximation" (By. D. R. Helman, G. G. Langdon, Jr., and J. J. Rissanen). The cited references are incorporated herein by reference to provide background information information.